The main parameters of the beam required to ignite a precompressed DT fuel, as foreseen by therecently proposed scheme of fast ignition by laser-accelerated protons (Roth et al 2001 Phys. Rev. Lett.86 436), are studied by 2-D numerical simulations and a simple model. For simplicity, instantaneous proton generation at distance d from the compressed fuel and exponential protonenergy spectrum, dn/dε∝exp (-ε/Tp), are assumed. An analytical expression and parametric numerical results are then given for the dependence of the minimum required beam energy on d, Tp and on the fuel density ρ. For the parameters of Roth et al (d≈4 mm; ρ≈400 g/cm3) the minimum total proton energy for ignition is about 40 kJ.